document.write( "Question 838253: solve the nth term for the following sequence 1,7,29,51,57
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Algebra.Com's Answer #505143 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The odd numbered terms form the arithmetic 1,29,57 with common difference 28.\r\n" );
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document.write( "So if we used only half that difference, 14, we would have the arithmetic\r\n" );
document.write( "sequence 1,15,29,43,57, which has the same odd-numbered terms but different\r\n" );
document.write( "even-numbered terms.  The nth term of that sequence is \r\n" );
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document.write( "Let's compare the sequences and observe how the even numbered terms\r\n" );
document.write( "of this sequence differ from the even numbered terms of the given sequence:\r\n" );
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document.write( "This sequence:        1,15,29,43,57 (arithmetic sequence, nth term 14n-13)\r\n" );
document.write( "Given sequence:       1, 7,29,51,57\r\n" );
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document.write( "Difference sequence:  0, 8, 0,-8, 0\r\n" );
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document.write( "So if we can think of a sequence that goes 0,8,0,-8,0,8,0,-8, ...  \r\n" );
document.write( "we can add it to the arithmetic sequence and we'll have the\r\n" );
document.write( "nth term of your sequence. Those are the x-intercept, maximum,\r\n" );
document.write( "x-intercept, minimum, x-intercept,...\r\n" );
document.write( "of the sine curve with amplitude 8\r\n" );
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document.write( "So the nth term is\r\n" );
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document.write( "That sequence is 1,7,29,51,57,63,85,107,113,...\r\n" );
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document.write( "Edwin

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